2017-2018Understanding A Fast Contour-Integral Eigensolver for Non-Hermitian MatricesB.S. Capstone
We examine a new complex contour integral-based eigensolver algorithm using ideas from functional analysis. This eigensolver algorithm extends previous eigensolvers that typically required some special structure, to an eigensolver that works on a more general class of complex-valued matrices.
The algorithm consists of two stages. First, it searches the complex plane for regions dense with eigenvalues. Second, it combs through those regions to find the eigenvalues using a modified form of the FEAST algorithm.
Due to time constraints we were only able to examine the first stage in detail, and for completeness provide a description for the second stage. Our work was exploratory in nature, which in practice consisted of building and testing a Matlab implementation of the first stage.